Planet Hunters X: Searching for Nearby Neighbors of 75 Planet and Eclipsing Binary Candidates from the K2 Kepler Extended Mission

We present high-resolution observations of a sample of 75 K2 targets from Campaigns 1-3 using speckle interferometry on the Southern Astrophysical Research (SOAR) telescope and adaptive optics (AO) imaging at the Keck II telescope. The median SOAR $I$-band and Keck $K_s$-band detection limits at 1" were $\Delta m_{I}=4.4$~mag and $\Delta m_{K_s}=6.1$~mag, respectively. This sample includes 37 stars likely to host planets, 32 targets likely to be eclipsing binaries (EBs), and 6 other targets previously labeled as likely planetary false positives. We find nine likely physically bound companion stars within 3" of three candidate transiting exoplanet host stars and six likely EBs. Six of the nine detected companions are new discoveries; one of the six, EPIC 206061524, is associated with a planet candidate. Among the EB candidates, companions were only found near the shortest period ones ($P<3$ days), which is in line with previous results showing high multiplicity near short-period binary stars. This high-resolution data, including both the detected companions and the limits on potential unseen companions, will be useful in future planet vetting and stellar multiplicity rate studies for planets and binaries.